A method for studying the qualitative dynamical properties of abstract computing machines based on the approximation of their program-size complexity using a general lossless compression algorithm is presented. It is shown that the compression-based approach classifies cellular automata (CA) into clusters according to their heuristic behavior, with these clusters showing a correspondence with Wolfram's main classes of CA behavior. A Gray code-based numbering scheme for initial conditions and a c

Tags:  chaos theory  ait  compression  wolfram's 4 classes  algorithmic information theory  cellular automata classification  phase transitions  lyapunov exponent  hypersensitivity  computer science  new ideas  dynamical systems